Non-Abelian Anyons and Topological Quantum Computation

@article{Nayak2008NonAbelianAA,
  title={Non-Abelian Anyons and Topological Quantum Computation},
  author={C. Nayak and Steven H. Simon and Ady Stern and Michael H. Freedman and Sankar Das Sarma},
  journal={Reviews of Modern Physics},
  year={2008},
  volume={80},
  pages={1083-1159}
}
Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate… 

Ternary logic design in topological quantum computing

A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state

Topological Quantum Computation with Non-Abelian Anyons in Fractional Quantum Hall States

We review the general strategy of topologically protected quantum information processing based on non-Abelian anyons, in which quantum information is encoded into the fusion channels of pairs of

Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure

Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit

Induced superconductivity in fractional quantum Hall edge

Topological superconductors represent a phase of matter with nonlocal properties which cannot smoothly change from one phase to another, providing a robustness suitable for quantum computing.

Topological Order in Superconductors and Quantum Hall Liquids

of “Topological Order in Superconductors and Quantum Hall Liquids” by Guang Yang, Ph.D., Brown University, May 2014 Fractional quantum Hall (FQH) liquids are interesting two-dimensional electron

Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states

We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors

Ab initio simulation of non-Abelian braiding statistics in topological superconductors

We numerically investigate non-Abelian braiding dynamics of vortices in two-dimensional topological superconductors, such as $s$-wave superconductors with Rashba spin-orbit coupling. Majorana zero

Topological Quantum Computing with Majorana Zero Modes and Beyond

Author(s): Knapp, Christina | Advisor(s): Nayak, Chetan | Abstract: Topological quantum computing seeks to store and manipulate information in a protected manner using topological phases of matter.

Competing ν = 5/2 fractional quantum Hall states in confined geometry

TLDR
Using measurements of tunneling between edge states, it is suggested that both the Abelian and non-Abelian states can be stable in the same device but under different conditions, and suggests that there is an intrinsic non- Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it.

Introduction to topological quantum computation with non-Abelian anyons

TLDR
This work aims to provide a pedagogical, self-contained, review of topological quantum computation with Fibonacci anyons, from the braiding statistics and matrices to the layout of such a computer and the compiling of braids to perform specific operations.
...

References

SHOWING 1-10 OF 413 REFERENCES

Geometric phases and quantum entanglement as building blocks for non-Abelian quasiparticle statistics

Some models describing unconventional fractional quantum Hall states predict quasiparticles that obey non-Abelian quantum statistics. The most prominent example is the Moore-Read model for the

Towards universal topological quantum computation in the ν = 5 2 fractional quantum Hall state

The Pfaffian state, which may describe the quantized Hall plateau observed at Landau level filling fraction $\ensuremath{\nu}=\frac{5}{2}$, can support topologically-protected qubits with extremely

Discrete non-Abelian gauge theories in Josephson-junction arrays and quantum computation

We discuss real-space lattice models equivalent to gauge theories with a discrete non-Abelian gauge group. We construct the Hamiltonian formalism which is appropriate for their solid-state physics

Topologically protected gates for quantum computation with non-Abelian anyons in the Pfaffian quantum Hall state

We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma et al., in a way that might potentially allow for the

Quasiholes and fermionic zero modes of paired fractional quantum Hall states: The mechanism for non-Abelian statistics.

  • ReadRezayi
  • Physics
    Physical review. B, Condensed matter
  • 1996
TLDR
The quasihole states of several paired states, the Pfaffian, Haldane-Rezayi, and 331 states, are studied, analytically and numerically, in the spherical geometry for the Hamiltonians for which the ground states are known exactly.

Topological quantum memory

We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and

Topological Quantum Computation

TLDR
The connection between fault-tolerant quantum computation and nonabelian quantum statistics in two spatial dimensions is explored and it is shown that if information is encoded in pairs of quasiparticles, then the Aharonov-Bohm interactions can be adequate for universal fault-Tolerance quantum computation.

Quantum groups and non-Abelian braiding in quantum Hall systems

Edge states and tunneling of non-Abelian quasiparticles in theν=5∕2quantum Hall state andp+ipsuperconductors

We study quasiparticle tunneling between the edges of a non-Abelian topological state. The simplest examples are a $p+ip$ superconductor and the Moore-Read Pfaffian non-Abelian fractional quantum

Topologically protected quantum bits from Josephson junction arrays

All physical implementations of quantum bits (qubits), carrying the information and computation in a putative quantum computer, have to meet the conflicting requirements of environmental decoupling
...